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There are lots of beautiful examples in it proving a great deal of nontrivial results by what are essentially elementary methods.
Have you looked at the problems section in the Mathematical Reflections?
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Problems are selected from all sorts of competitions throughout the world including the IMO, various national selection tests for the IMO, and of course the Putnam itself.
By Abhi: Good aspects of this book have been said by most of the other reviewers.
The main problem with such books is that for slightly experienced problem solvers, this book probably does not provide a whole lot of information as to what needs to be done to get better.
For instance, for a kid who is in 10th grade struggling with math, this is a very good book.
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